This is the set up I used with my FT-2800 while testing a homebrew antenna. On the right are two 12V gel cell batteries out of an old UPS. They are hooked in parallel. In the center is the radio, this unit has the same basic power requirements as the FT-8800. On the left is my SWR meter hooked in line with the antenna I was testing, you wouldn't need that after the antenna was trimmed. For your application I would consider a homebrew 1/4 wave with three or more ground radials mounted at the base and angled down about 45°. You can find plans on the internet for this antenna pretty easy and it only cost a few dollars to build.
All of this stuff could be built into an ammo can, something slightly bigger than the 50Cal int the picture.
One question for you, why not hard mount the FT-8800 in your truck and get a hand held. One of the best features of the FT-8800 is it's cross band repeat capability. I've used the feature* and it's very cool, I can go hiking around and use my truck radio as a repeater.
*I have the FT-8900 same radio as the FT-8800 with more bands.